Localization of spherical nanoparticles within lamellar AB diblock copolymer melts through self-consistent field theory

Here we report the results of a three dimensional hybrid self-consistent field theoretic (HSCFT) model describing the equilibrium particle distribution of spherical nanoparticles within symmetric AB diblock copolymer melts. Holding the polymer composition and morphology fixed, we consider a comprehensive parameter space comprised of the Flory interaction parameter describing interactions between B segments and the particle surface compared to the segment-segment interaction parameter (χBP/χAB), the particle volume fraction (?_P), and the ratio of the particle diameter to block copolymer domain spacing (dP/dAB). Analysis of the free energy over this parameter space yields phase diagrams showing the conditions under which particles segregate to the intermaterial diving surface (IMDS) or the center of the domain. Interestingly, w e predict a particle concentration-dependent “reentrant” phase transition in which particles move from the domain interior, to the IMDS, and back as ?_P increases. These results are interpreted as a subtle consequence of the competition between enthalpic polymer-particle interactions and the chain packing frustration imposed by the particulate inclusion. These results are consistent with recent experiments on block copolymer nanocomposites.